History offers only two models for the integration of different countries, with competing national interests and rival strategic ambitions, into a single, unified economic and political system. There is conquest and there is the European Union.

Some of the EU's more hysterical critics don't see much difference between the two. But in reality, there is something superb in the agreement by European nations to set aside centuries of slaughter, and create a single marketplace whose rules are decided by collaboration and compromise. It is the only miracle ever performed by committee.

That, in essence, is the European Idea. It is not a destination but a trajectory – from atavistic nationalism to co-operative internationalism. The assumption has been that "ever-closer union", as mandated by the 1957 Treaty of Rome, must be desirable because the alternative would be a relapse into ever-wider disunion, a path forbidden by atrocious history. So the crisis currently afflicting the euro is not just financial, it is existential. Never before has one of the EU's grand projects looked so close to going into reverse.

Greece, whose bodge-job finances triggered the crisis, might well be forced to negotiate an exit from the euro. Diplomats, economists and politicians who dismissed that scenario as too complex and too destabilising a few months ago now debate the detail of how it might work. Rarely has the unthinkable so quickly become the thought.

That doesn't mean the single currency is doomed. Last week, eurozone finance ministers gambled hundreds of billions in bailout funds that it is not. But alongside the financial turmoil is a growing political crisis and it afflicts not just the euro but the whole European project.

EU governments are used to disagreements over economic co-operation, but they were totally unprepared for the vast financial transfers – bank bailouts, fiscal stimulus, emergency loans – that were required in the last two years to avert economic meltdown. It has been especially difficult for Germany, which has observed stricter budget discipline than many of its more wastrel neighbours, and resents being tapped up to rescue them.

The mood among many Germans was summarised by a recent headline in Bild, the country's most popular newspaper, bemoaning that the euro bailout made the nation "the suckers of Europe again". That expresses the natural resentment that taxpayers' money is going to subsidise unsustainable public sector jobs for Greeks who have lived way beyond their means, when there are plenty of needy Germans who haven't.

But the fact that such frustration is readily vented also reflects a cultural change in Germany's relationship with the rest of Europe. For most of the second half of the 20th century, West Germany integrated itself with its neighbours in a spirit of repentance for the Second World War. The ideal of European economic unification was a way to pursue national ambitions, but stripped of toxic notions of Teutonic pre-eminence.

There is only so long that any country, whatever the crimes of its past, can sustain an economic and foreign policy characterised by atonement. For Germany, that limit has been reached.

Germany is not about to turn Eurosceptic on the petulant British model. If anything, Berlin will now press ahead with deeper integration inside the eurozone, but on its own terms, with stricter rules, more rigorously enforced. That, according to German finance minister Wolfgang Schäuble, "naturally means a bit of federalism in the German sense of federal".

The UK will never sign up to that, but it isn't in the euro anyway. France is, but Paris prefers European integration when it creates institutions that are more Gallic-looking. In fact, most member states will bridle at the idea that the EU should form an inner core designed by the Bundesbank.

So there will now be period of dense technical negotiation, beset by national rivalries and acrimonious diplomacy. It is hard to overstate how disastrous that is for the European project. It guarantees that the one thing Brussels will fail to do is act with a unity of purpose in dealings with the rest of the world. The hope of being able to do just that was the only thing that sustained the EU through its last crisis – the gruesome ratification of the Lisbon treaty.

That process, in which European leaders haggled with their electorates in a series of bizarre referendums, reinforced every conceivable prejudice about the contempt of European elites for popular opinion. It was justified by the expectation that, once the new reforms were in place, the EU might begin to legitimise itself by its good deeds in the world.

Together, European governments would constitute a superpower, ready to deal on equal terms with the US and to check the flight of economic power eastwards, to China and India. The European Idea would be rejuvenated because citizens would start to witness the benefits of integration as Brussels set the global agenda on climate change, financial regulation, human rights, world peace. There was no plan B.

A neat summary of plan A is contained in the recent findings of the Reflection Group, a team of distinguished business leaders, academics and elder statesmen commissioned by European governments to consider the strategic challenges on the horizon. Their report, published two weeks ago, talked about reconnecting the EU with its citizens, investing in skills, a "new industrial revolution" (green, naturally), speaking with one voice in the world.

The group warns that "the choice for the EU is clear: reform or decline". That is too optimistic. Reform is what the EU has always done. Perpetual, incomprehensible reform is one reason why many Europeans don't like the EU and don't know any longer what it is for. The point of the Lisbon treaty was that it should be the reform to end all reforms. And just when the EU most needs to move on from arcane debate about its structures and start actually doing things, it is plunged into the worst crisis of internal cohesion in its history.

The EU will continue to muddle through, but the credit crunch has buried the European Idea. The moral authority contained in the vast achievement of binding Europe's bellicose tribes into peaceful collaboration is spent. There will be no 21st-century European superpower, just a bunch of middle-sized ex-powers arguing over a dwindling pot of devalued money. Reform or decline? Europe will do both.